United States

Department of

Agriculture

Forest Service

Pacific Northwest

Research Station

General Technical

Report

PNW-GTR-574

April 2003

WestPro:

A Computer Program for

Simulating Uneven-Aged

Douglas-fir Stand Growth and

Yield in the Pacific Northwest

Rebecca Ralston, Joseph Buongiorno, Benedict Schulte,

and Jeremy Fried
Rebecca Ralston is a research assistant, Joseph Buongiorno is a professor, and

Benedict Schulte is a research assistant, Department of Forest Ecology and Management, University of Wisconsin, Madison, WI 53706; Jeremy Fried is a research forester, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research

Station, P.O. Box 3890, Portland, OR 97208-3890.

Authors
Ralston, Rebecca; Buongiorno, Joseph; Schulte, Benedict; Fried, Jeremy. 2003.

WestPro: a computer program for simulating uneven-aged Douglas-fir stand growth

and yield in the Pacific Northwest. Gen. Tech. Rep. PNW-GTR-574. Portland, OR :

U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station.

25 p.

WestPro is an add-in program designed to work with Microsoft Excel to simulate the

growth of uneven-aged Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) stands in the

Pacific Northwest region of the United States. Given the initial stand state, defined as the

number of softwood and hardwood trees per acre by diameter class, WestPro predicts

the future stand state for each year of a predetermined time horizon. Management regimes are defined by a target stand distribution and a cutting cycle. Performance indicators include diversity of tree size and species, timber yield, and net present value of

harvest over the given horizon.

This paper contains background information on the WestPro program and instructions

and suggestions for its application. By working the examples found in the text, the user

will learn how to simulate the growth of a given initial stand and to predict how different

management regimes may affect stand structure, yield, and diversity. Limitations of the

model also are discussed.

Keywords: Douglas-fir, Pseudotsuga menziesii, uneven-aged, management, economics,

ecology, WestPro, simulation, software, growth model, diversity.

Abstract
1 1. Introduction and Background Information

1 Before Beginning

1 What is WestPro?

1 Why Simulate This Type of Stand?

1 How Does WestPro Work?

1 2. Getting Started

1 Installing the WestPro Software

2 The WestPro Menu

2 3. A Basic WestPro Simulation

2 The Input Data Worksheet

4 The Stand Development Worksheet

5 The Production Worksheet

6 4. Managing Data in WestPro

6 Storing Data in WestPro

7 Deleting Stored Data

7 Retrieving Stored Data

8 5. Advanced WestPro

8 The BDq Calculator

9 Creating Charts

13 The Stock-and-Cut Table

16 Running Multiple Simulations

17 Interpreting the Examples

18 6. Troubleshooting and Further Program Applications

18 Model Restrictions

18 Program Restriction

18 Further Applications of WestPro

18 Acknowledgments

19 Metric Equivalents

19 Literature Cited

20 Glossary

21 Appendix A–WestPro Data

23 Appendix B–WestPro Model and Parameters

Contents
1

This paper provides background, instructions for using WestPro, and additional suggestions for application of the program. The instructions go through each step of the examples (located in boxes throughout the manual). If you are new to WestPro, it will be

useful to run these examples while reading the paper.

This section describes WestPro’s purpose and background, section 2 shows how to

install the program and use the WestPro menu, section 3 offers instructions for performing basic, single-stand simulations, section 4 discusses how to store and retrieve data,

and section 5 provides instructions on using the more advanced features of the program.

Users who are unfamiliar with Microsoft Excel may also want to consult the Microsoft

Excel User’s Guide for additional help.

WestPro is a computer program designed to simulate the growth of uneven-aged

Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) stands over time. With this program,

different management regimes can be considered, and their outcomes can be predicted

quickly. WestPro is a useful tool for suggesting which management should be implemented. Similar programs, such as SouthPro for loblolly pine (Pinus taeda L.) in the

Southern United States (Schulte et al. 1998), and NorthPro for hardwood stands in the

Lake States (Kolbe 1998), have already been developed. The WestPro software was

designed and calibrated for uneven-aged Douglas-fir stands in the Pacific Northwest region of the United States.

Timber production is a primary goal for a large portion of Douglas-fir stands, but at the

same time, concerns about sustainability and negative biological impacts are being

raised as a result of the visible adverse effects of current management practices (Curtis

and Carey 1996, Curtis and Marshall 1993). Because interest in silvicultural alternatives

to even-age management of Pacific Northwest forests is increasing, better information is

needed on the effects of these alternatives (Emmingham 1998). WestPro is meant to

add to the “toolkit” of foresters a method for predicting how a given stand might look in

the future, and what it might yield under uneven-age management.

The WestPro program uses a density-dependent matrix model calculated from data

for 66 uneven-aged Douglas-fir plots. The plots were in western Oregon and western

Washington and were measured by the Forest Inventory and Analysis Program of the

USDA Forest Service, Pacific Northwest Research Station (PNW-FIA). Each plot was

measured twice over an interval of approximately 101⁄2 years. Simulations with the

WestPro model have produced, without apparent bias, results replicating the growth on

the observed plots, and long-term projections consistent with prior knowledge of unevenaged Douglas-fir stands (Ralston et al., in press).

The matrix model built in WestPro predicts growth, mortality, and the rate of regeneration

for softwoods and hardwoods as a function of basal area, site index, and individual tree

size when those variables are statistically significant. For details regarding the model

data, form, and parameters, see appendices A and B.

WestPro is an add-in program that works with Microsoft Excel for Windows.1

 You will

need at least 16 megabytes of random access memory (RAM) to run WestPro. This

program works for most versions of Windows (from Windows 3.1 through Windows XP)

and Excel (from Excel 5.0 to Excel 2000).

1. Introduction and

Background

Information

Before Beginning

What is WestPro?

Why Simulate This Type

of Stand?

How Does WestPro

Work?

 2. Getting Started

Installing the WestPro

Software

1

 The use of trade or firm names in this publication is for

reader information and does not imply endorsement by

the U.S. Department of Agriculture of any product or

service.
2

To install the software, follow these steps:

• Insert the diskette or compact disk (CD) containing the WestPro Microsoft Excel

add-in.

• Open Microsoft Excel and start a new workbook.

• Under the Tools menu, select Add-ins. Once the add-ins dialog box appears, select

Browse and choose the WestPro add-in (WestPro.xla) from the drive containing the

diskette or CD. Click OK.

• The window that appears asks if you would like to copy WestPro to the add-ins folder

on your hard drive. Click OK.

• The WestPro program will appear in the list of the add-ins dialog box. Be sure the

box corresponding to the WestPro add-in is checked and click OK.

• Return to the Tools menu and notice that WestPro is now the last choice in the

menu. Select WestPro and click OK in the title box. A new box will appear, asking

you if you want the Input Data worksheet inserted. Click Yes to insert the new

worksheet.

• The WestPro menu appears before the File menu of the Excel menu bar.

While WestPro is running, all Excel functions are still available. Once WestPro is installed, it will remain an option under the Tools menu every time Excel is opened. To

uninstall WestPro, you must uncheck the corresponding box in the Add-ins list and quit

Excel.

The WestPro menu, in the upper left corner of the Excel menu bar, has seven options

(fig. 1). To stop the WestPro program and remove the menu, click the last option, Quit.

After you have quit the program, any worksheets you have added with WestPro will still

be present, but no WestPro function can be carried out without again starting WestPro

under the Tools menu.

The other six menu items are WestPro functions. Five have submenus, and under these

you will find additional functions. Figure 1 shows the WestPro menu and one of the

submenus.

While the program is running, the WestPro menu is present in all the workbooks open in

Excel. Thus, you can work with several simulations, in different workbooks, at the same

time.

Use the Input Data worksheet (fig. 2) to enter data about the stand you want to simulate

and the management you will use. WestPro is for uneven-aged Douglas-fir forests, and

recognizes two species groups, softwoods and hardwoods.

The initial distribution refers to the number of trees per acre, by species group, by 2-inch

diameter classes (fig. 2). For example, the diameter class labeled “4” includes all trees

with diameters greater than or equal to 3 inches and less than 5 inches.

The target distribution refers to the number of trees per acre, by species group, and by

size class that should remain after harvest (fig. 2). A target of zero instructs WestPro to

harvest all trees in that size class; you can prevent the removal of any tree by entering a

very high target, say 1,000. When there are more available trees than the target value,

then the harvest is the difference between the available trees and the target.

The WestPro Menu

 3. A Basic WestPro

Simulation

The Input Data

Worksheet
3

Stumpage prices for sawtimber are by unit of volume and by size class, whereas for

pulpwood they are by weight only. The management schedule data include the first year

of the simulation, the year of the first harvest, the cutting cycle (interval between harvests), and the length of the simulation. The cutting cycle must be at least 2 years, even

if there is no harvest.

Other input data include the fixed costs (costs of re-entry at each harvest, independent

of the harvest), the interest rate, the site index (King 1966), and the state (OR or WA).

When you run a simulation, WestPro considers any empty input data cell an error and

will prompt you to fix it. You can enter zero for price, fixed cost, and interest rate if you

are not interested in financial information.

Figure 1—The WestPro menu.

Figure 2—The Input Data worksheet, containing the data to run example 1.
4

The Stand Development worksheet gives the expected number of trees per acre by diameter class and species group for each successive year. Figure 3 shows the part of the

Stand Development worksheet containing the diameter distribution of softwoods, for the

first 27 years from example 1.

Figure 3—Part of the Stand Development worksheet showing the diameter distribution of

softwoods over time (example 1).

The Stand Development

Worksheet

Example 1: A Single Simulation

Manually enter or copy the data in figure 2 into the Input Data worksheet on your computer. To copy the data, open the Excel workbook named “Data for Example 1” located

on the WestPro diskette or CD. Copy and paste ranges B5:T8, B12:T15, and B18:B29

from the Data for Example 1 worksheet to the same location in your blank Input Data

worksheet.

In this example, the initial distribution corresponds to the average diameter distribution

of the plots in western Washington used to develop the WestPro model. The target

distribution for softwoods is the same as the initial distribution, whereas the target

distribution for hardwoods results in the removal of all trees larger than 11 inches in

diameter. The sawtimber and pulpwood prices were typical for the region in 1999

(Warren 2001). To perform a single simulation, select WestPro→Single

Simulation→Run. The results of the simulation are stored in two new worksheets,

Stand Development and Production.
5

Figure 4—Part of the Stand Development worksheet showing the summary statistics

(example 1).

If you scroll right, past the diameter distributions for both species groups, you will find

the summary statistics, including the stand basal area, basal area by species groups,

species group diversity and size class diversity for each year (fig. 4). The species group

and size class diversity indices are based on basal area and measured by Shannon’s

Index (Pielou 1977, Shannon and Weaver 1963). Highest species group diversity occurs

when there is the same basal area in each species group, and highest size diversity

when there is the same basal area in each size class.

The Production worksheet (fig. 5) shows data for each harvest in terms of basal area

cut, gross income, and the pulpwood and sawtimber volumes cut for each species

group. The volumes are computed from equations linking tree volume to tree diameter

and stand basal area (see app. B). The spreadsheet also shows the net present value of

each harvest, the total net present value, and the annual production in basal

area and volume cut.

The Adjustable values box allows you to see the effect of different interest rates or fixed

costs, without having to rerun the simulation. The Production worksheet also shows the

input data, as a reminder of the assumptions made in this simulation.

The Production

Worksheet
6

The previous section discussed a basic WestPro simulation, which is sufficient if you

only want to do one simulation. In that case, you can save the input data and results of

a single simulation as an Excel file by choosing File→Save As and giving an appropriate name to the workbook. If, however, you would like to examine the effects of changing

some of the simulation parameters and run several simulations, you may find it more

efficient to manage data with the Setup Files feature of WestPro than to repeatedly set

up and save individual simulations.

For that purpose, once you have entered data in the Input Data worksheet, you can store

them for later use. When you store data, you are copying them from the Input Data worksheet to the Setup Files worksheet. The Setup Files worksheet acts as a holding area

for all the data you have stored. It also contains data sets built into the program. The

Setup Files worksheet is not visible, and you do not need to see it, but if you would like

to view it, see the instructions in section 6.

Figure 5—The Production worksheet for example 1.

4. Managing Data in

WestPro

Storing Data in WestPro
7

Give detailed names to setup files. If you save many files, a detailed name will help you

choose the correct file when you want to retrieve it.

To delete setup files, choose WestPro→Setup Files→Delete. Select the field that you

want to delete a file from, and highlight that file in the list. After you hit Delete, only that

file is removed from the Setup Files worksheet.

Selecting WestPro→Single Simulation→Setup opens the Load Setup Files window

(fig. 7). With this window, you can copy data from the Setup Files worksheet to the Input

Data worksheet. If you have not added any data to the Setup Files worksheet, only the

built-in data will be available.

To select the data to load into the Input Data worksheet, highlight the file name in the

Initial Distribution list, the Softwoods Target list, and the other lists. To select the default

interest rate, site index, or state, place a checkmark in the Insert box. You can change

the default values by typing your choice in the respective text box. Click OK to copy the

selected setup files to the Input Data worksheet.

Example 2: Adding Setup Files

Select WestPro→Setup Files→Add. WestPro will ask you if you would like a copy

of the Setup Files worksheet inserted. Click Yes. The Add Setup Files window (fig. 6)

should appear on your screen.

Check the Add the Target Distribution box, make sure that softwoods are selected,

and name the softwood target distribution “Average WA SW.”

Check the Add the Management Schedule box and name it “Start 0,Cut 5,Cycle

20,205 Yr.”

Check the Add the Fixed Costs box and name it “10.” Click OK.

As each file is copied, you may choose its position in the list of files. The names already shown in the lists are the setup files built into WestPro. Insert your setup files at

the top of each list.

You need not copy the initial distribution, the hardwood target distribution, or the

prices because they are built in as “Average WA plots,” “11 inch max. diameter,” and

“Example Price 1,” respectively.

Figure 6—The Add Setup Files

window (example 2).

Deleting Stored Data

Retrieving Stored Data
8

To preview the data before loading them, click the appropriate button in the Preview selection box and click the Show button at the top of the window. For example, clicking

Show in the window in figure 7 would show the initial distribution in the file named Average WA plots.

This calculator is meant to calculate the number of trees by size class in a stand with

a specific BDq distribution (see “Glossary”) (Smith 1997). The q-ratio is the ratio of the

number of trees in successive size classes.

Going to WestPro→ Setup Files→BDq Distributions opens the BDq calculator (fig. 8).

Use the arrow buttons to set the basal area (ft2

/acre), the maximum diameter (in), the qratio, and the minimum diameter (in) to the desired level, then click the Calculate button. Figure 8 shows the number of trees in each size class that would give a basal area

of 125 ft2/ac, with trees of diameters from 3 to 31 in, and a q-ratio of 1.4.

You can copy the calculated distribution to the Input Data worksheet as the initial distribution or as the target distribution for either softwoods or hardwoods by selecting the

destination and clicking the Copy button. Clicking the Cancel button closes the calculator window.

Figure 7—The Load Setup Files window.

5. Advanced

WestPro

The BDq Calculator

Figure 8—The BDq Distribution Calculator window.
9

WestPro lets you create charts with data from the Stand Development worksheet and

from the Production worksheet. Under the WestPro menu there are two headings, Stand

Development Charts and Production Charts, each containing different chart types. To

create one of the Stand Development charts, the Stand Development worksheet (figs. 3

and 4) must be visible; otherwise WestPro will prompt you to put this sheet in front.

Similarly, to create a Production chart, the Production worksheet (fig. 5) must be visible.

There are four stand development charts:

• Size diversity (Shannon index)

• Species diversity (Shannon index)

• Size distribution (trees/acre)

• Stand basal area (ft2/acre)

There are three production charts:

• Basal area cut (ft2

/acre)

• Gross income ($/acre)

• Volume cut (ft3/acre)

The seven chart types are shown in figures 9 through 15. You can choose the year or

range of years of the data. For the size distribution (fig. 11b) and stand basal area (fig.

12) charts, you also can select the species groups to plot, and for the volume cut chart,

you can select the species and product (fig. 15a) to plot.

Creating Charts

Figure 9—Chart of size diversity.
10

Figure 10—Chart of species

group diversity.

Figure 11a—Size Distribution Chart window

(example 3).

Figure 11b—Chart of size distributions (example 3).
11

Figure 12—Chart of stand basal

area.

Figure 13a—Basal Area Cut Chart window

(example 4).

Figure 13b—Chart of basal area cut (example 4).
12

Figure 14—Chart of gross

income.

Figure 15a—Volume Cut Chart window.

Figure 15b—Chart of volume cut.
13

Highlighting one year in the Size Distribution Chart window will plot the distribution for a

single year. To plot sequential years, highlight the first year, press the Shift key, and then

click the last year to plot all of the years between. To plot multiple, nonsequential years,

click each year to plot while holding down the Ctrl key.

Example 4: Charting Basal Area Cut

To get a bar chart of the basal area cut at each harvest, do the following. With the Production worksheet produced by example 1 in the foreground, select

WestPro→Production Charts→Basal Area Cut. When the Basal Area Cut Chart

window appears (fig. 13a), leave the default selection (First Year: 5, Last Year: 205) as

the years to plot. Click OK and name the chart “BACut” (fig. 13b).

The Stock-and-Cut table gives information on the immediate effects of harvesting a particular initial stand to a target stand, and on how to do the harvest. The Stock-and-Cut

table in figure 16 (on two pages) shows the initial stand and its annual growth (predicted

by WestPro), the target stand and its annual growth, and the residual stand after harvest

and its annual growth. The marking guide in the last column shows how the pole, small

sawtimber, medium sawtimber, and large sawtimber trees should be selected for harvest.

Example 5: Generating a Stock-and-Cut Table

To get the Stock-and-Cut table in figure 16, with the year 25 stand obtained in example

1 as initial stand, and the target stand in example 1, do the following. With

the Stand Development worksheet produced by example 1 in the foreground, select

WestPro→Stock-and-Cut Table. In the Stock-and-Cut Table window (fig. 17a), click

the Stand Development button to select that worksheet as the location of the initial

and target stand distributions.

Next, in Stock-and-Cut Stand Development Selection window (fig. 17b), choose the

Initial Distribution year of 25, and leave the selected Target Distribution as Target. Click

Table to generate the Stock-and-Cut table in a new worksheet. Click Cancel to close

the Stock-and-Cut Table window.

From the Stock-and-Cut Table window (fig. 17a), you also can choose data in the Setup

Files or Input Data worksheets. Choosing the Input Data worksheet as the data source

selects the preharvest and target distributions on that worksheet. Choosing the Setup

Files worksheet as the data source opens a window that allows you to choose from the

distributions in that worksheet (see section 4, “Storing Data in WestPro”).

Example 3: Charting Size Distribution

To chart size distribution for hardwoods and softwoods the year before and after the

second harvest, do the following. With the Stand Development worksheet produced by

example 1 in the foreground, go to WestPro→Stand Development Charts→Size

Distributions. When the Size Distribution Chart window (fig. 11a) appears, highlight

year “25,” press the Shift key, then highlight year “26” also. Check both species

groups. Click OK, and name the chart “SizeDist25,26” when prompted (fig. 11b).

The Stock-and-Cut Table
14

Figure 16—Stock-and-Cut table

(example 5).
15

Figure 16—Stock-and-Cut table

(example 5), continued.
16

Figure 17a—Stock-and-Cut Table window.

Figure 17b—Stock-and-Cut Stand Development Selection window (example 5).

You can run many simulations sequentially. The results of each simulation are saved in a

separate workbook containing only the Stand Development and Production worksheets.

Example 6: Running a Batch of Simulations

Note: The data used in this example will only be available if you have done the previous

examples.

Choose WestPro→Multiple Simulations→Setup. Click Yes when asked if you would

like the Batch File worksheet (fig. 18) inserted. The Update Batch File window (fig. 19)

will appear on your screen. Highlight “Average WA plots” as the initial distribution, “Average WA SW” as the softwoods target, “11 inch max. diameter” as the hardwoods

target, “Start 0,Cut 5,Cycle 20,205Yr” as the management schedule, “Example Price 1”

as the stumpage prices, and “10” as the fixed costs. Leave the interest rate, site index,

and state at the default settings of 3, 96, and WA, respectively. Click the ADD button.

Change the interest rate to 5 (percent per year) and click ADD. Next, change the site

index to 115 (feet) and click ADD again. Finally, change the Hardwoods Target to “7

inch max. diameter” and click ADD, then click Close to close the window.

Choose WestPro→Multiple Simulations→Run. Click Yes to confirm, then select a

destination drive and save each simulation as the default name (in the last column of

fig. 18) by clicking Save. Click Yes to run the batch of simulations. The final batch

worksheet should look like figure 18, but the locations of your saved workbooks may

be different.

Running Multiple

Simulations
17

In the upper left corner of the Update Batch File window (fig. 19) is a run number that

corresponds to the simulation number in the Batch File worksheet (fig. 18). When first

preparing a set of simulations to run, start with run number 1. After setting up a file and

clicking ADD, the Update Batch File window remains open to setup run number 2, and

this continues until you click Cancel. Notice the cells labeled “First simulation to run”

and “Last simulation to run” at the top of the Batch File worksheet. These fields will automatically adjust to the number of batches you add. However, if you want to run only certain sequential simulations, you can manually enter the run numbers in those fields of

the worksheet.

After working out the examples, you should have a better understanding of WestPro’s

capabilities. You can look at the predictions on worksheets and charts to determine if

the stand structure is sustainable over time. The examples presented in this paper exhibit an increase in size diversity (fig. 9) but a decrease in species group diversity (fig.

10) over time, while the stand basal area (ft2

/acre) decreases at first and then reaches a

sustainable level (fig. 12). Also, the production predictions reveal that the total basal area

cut (ft2/acre), gross income (dollars/acre), and volume cut (ft3/acre) reach steady levels

over time (figs. 5, 13b through 15). The above examples represent only one possible

management regime for an uneven-aged stand. You can use WestPro to investigate

others.

Figure 18—Batch File worksheet (example 6).

Figure 19—Update Batch File window (example 6).

Interpreting the

Examples
18

The WestPro software is intended to serve as a guide for the management of unevenaged Douglas-fir stands. Its equations represent the expected development of stands

based on observations from 66 plots on wide-ranging sites in Washington and Oregon.

Thus, like other models, WestPro predicts average expected values. Although it may not

predict accurately the observed growth and yield on an individual stand, its predictions

should be close to the average growth and yield over many stands (Ralston et al., in

press).

The WestPro program automatically corrects errors, or prompts users to correct errors

in data entry. However, some errors may still go undetected. The following information

will help you prevent or correct those errors.

Many of the worksheet cells in which you need not enter or change data are protected.

This protection can be removed by going to the Tools→Protection→Unprotect Sheet.

You will be prompted to enter a password, “Douglas-fir.” If you remove the protection,

you will be able to make changes in the sheet format. However, WestPro is designed to

reference particular cells or ranges of cells. Any change to the format could produce an

error or unintended results.

You can view the data in the Setup Files worksheet by going to Format→Sheet→

Unhide. When the Unhide window opens, choose Setup Files and that sheet will now

be visible. If you change the format or enter data directly into the Setup Files worksheet,

however, it will most likely result in an error.

Other errors can result when the management schedule does not make sense. WestPro

is prepared for many errors of this kind and will instruct you on how to correct the problem. WestPro does have restrictions on the management schedule parameters. The

maximum length of simulation is 2,000 years, no more than 254 harvests can be performed, and you must enter a cutting cycle greater than 1 year. Also, you cannot run

more than 500 batch simulations at one time.

This manual does not suggest a particular management regime for uneven-aged

Douglas-fir stands, but using the WestPro software may help you choose a regime,

based on the predicted economic and ecological consequences of different approaches.

Although the example used in the paper has emphasized only a few methods of setting

target distributions, target distributions of any shape could be investigated with WestPro.

Coupled with the flexibility of setting cutting cycles, and targeting hardwoods as well as

softwoods, WestPro is a tool with a wide range of applications for multipurpose forestry

in the Pacific Northwest.

The research leading to this paper was supported, in part, by the USDA Forest Service,

Pacific Northwest Research Station, Forest Inventory and Analysis Program, by USDACSREES grant 2001-35108-10673, and by the School of Natural Resources, University

of Wisconsin, Madison. We thank Bryan Lu, Tara Barett, and Ed deSteiguer for their

comments on WestPro and this users manual, while we take sole responsibility for the

final products.

6. Troubleshooting

and Further Program

Applications

Model Restrictions

Program Restriction

Further Applications of

WestPro

Acknowledgments
19

When you know: Multiply by: To find:

Inches (in) 2.54 Centimeters

Feet (ft) .304 Meters

Square feet (ft2

) .0929 Square meters

Cubic feet (ft3) .0283 Cubic meters

Acres (ac) .405 Hectares

Square feet per acre (ft2/ac) .2293 Square meters per hectare

Cubic feet per acre (ft3/ac) .06997 Cubic meters per hectare

Trees per acre 2.471 Trees per hectare

Curtis, R.O.; Carey, A.B. 1996. Timber supply in the Pacific Northwest: managing for

economic and ecological values in Douglas-fir forests. Journal of Forestry. 94(9): 4-7,

35-37.

Curtis, R.O.; Marshall, D.D. 1993. Douglas-fir rotations—Time for reappraisal? Western

Journal of Applied Forestry. 8(3): 81-85.

Emmingham, B. 1998. Uneven-aged management in the Pacific Northwest. Journal of

Forestry. 96(7): 37-39.

King, J.E. 1966. Site index curves for Douglas-fir in the Pacific Northwest.

Weyerhaeuser For. Pap. 8. Centralia, WA: Weyerhaeuser Forest Research Center.

49 p.

Kolbe, A.E. 1998. A growth model for Wisconsin’s and Michigan’s northern hardwoods,

and management implications. University of Wisconsin-Madison. 163 p. M.S. thesis.

Kolbe, A.E.; Buongiorno, J.; Vasievich, M. 1999. Geographic extension of an unevenaged, multi-species matrix growth model for northern hardwood forests. Ecological

Modeling. 121: 235-253.

Lin, C.; Buongiorno, J.; Prestemon, J.; Skog, K. 1998. Growth model for unevenaged loblolly pine stands. Res. Pap. FPL-RP-569. Madison, WI: U.S. Department of

Agriculture, Forest Service, Forest Products Laboratory. 13 p.

Pielou, E.C. 1977. Mathematical ecology. Toronto, ON: John Wiley and Sons. 385 p.

Ralston, R.E.; Buongiorno, J.; Schulte, B.; Fried, J. [In press]. Growth and yield

model for uneven-aged Douglas-fir stands in the Pacific Northwest, with management

applications. International Transactions of Operations Research.

Schulte, B.; Buongiorno, J.; Lin, C.R.; Skog, K. 1998. SouthPro: a computer program

for managing uneven-aged loblolly pine stands. Gen. Tech. Rep. FPL-GTR-112.

Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products

Laboratory. 47 p.

Shannon, C.E.; Weaver, W. 1963. The mathematical theory of communication.

Urbana, IL: University of Illinois Press. 117 p.

Smith, D.M. 1997. The practice of silviculture: applied forest ecology. 9th ed. New York:

John Wiley and Sons. 537 p.

Warren, D.D. 2001. Production, prices, employment, and trade in Northwest forest

industries, all quarters 1999. Resour. Bull. PNW-RB-235. Portland, OR: U.S.

Department of Agriculture, Forest Service, Pacific Northwest Research Station. 171 p.

Metric Equivalents

Literature Cited
20

BDq distribution—A diameter distribution defined by stand basal area (ft2/acre), maximum and minimum tree diameters (in), and a q-ratio, the ratio of trees per acre in a diameter class to the number of trees per acre in the next larger class.

Cutting cycle—The time interval between successive harvests in an uneven-aged stand.

DBH—The diameter of a tree recorded at breast height.

Fixed costs—The costs per acre not included in the stumpage price.

Initial distribution—The number of trees per acre in each diameter class, for both species groups, at year zero.

Management schedule—The time parameters of the stand simulation, including the

first year of simulation, year of first harvest, the cutting cycle, and the length of the simulation.

Marking guide—The portion of the Stock-and-Cut Table that indicates the number of

pulpwood and sawtimber trees that are cut from the initial distribution as dictated by the

target distribution.

Net present value—The net revenue (gross income minus fixed costs), discounted to

the present.

t r

R C NPV

(1+ )

− = ,

where R is the gross income (dollars/acre), C is the fixed cost (dollars/acre), r is the real

interest rate (percent/year), and t is the number of years in the future. The total net

present value is the sum of the net present value over all harvests.

Pulpwood—All softwood trees with a diameter smaller than 9 inches and all hardwood

trees with diameters smaller than 11 inches.

Sawtimber—Trees large enough to produce sawlogs. All softwood trees with a diameter

of 9 inches or larger and all hardwood trees with diameter of 11 inches or larger.

Site index—The average height of the five dominant Douglas-fir trees at 50 years of age.

Original database measurements used King’s selection method (King 1966).

State—The state where your stand is located, either Washington (WA) or Oregon (OR).

The distinction is made because, all other things being equal, hardwoods in Washington

grow faster than in Oregon, according to the data used to develop the growth equations.

Target distribution—The number of trees per acre, by diameter class and species

group, desired after each harvest.

Glossary
21

This appendix summarizes the data used to develop the equations for the density-dependent matrix model used in the WestPro program. More detail on the data, equations, and

model estimation and validation can be found in Ralston et al. (in press).

The data came from sample plots in Oregon and Washington measured by the Forest

Inventory and Analysis Program (FIA) at the USDA Forest Service, Pacific Northwest

(PNW) Research Station. All the plots had been measured at two successive inventories.

The most recent inventory was conducted in 2000 in the state of Washington and between 1995 and 1997 in Oregon. The previous inventories occurred between 1988 and

1990 in Washington, and between 1984 and 1986 in Oregon.

The selected plots had the following characteristics: the primary forest type was

Douglas-fir, the plot had been measured twice, and it was classified as timberland

and uneven-aged. This gave 43 plots in Oregon and 23 in Washington.

Trees with a diameter at breast height of more than 3 inches were used to estimate

model equations. The trees were grouped into softwoods or hardwoods. The primary

softwood species were Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) and western

hemlock (Tsuga heterophylla (Raf.) Sarg), and the most common hardwoods included

bigleaf maple (Acer macrophyllum Pursh), red alder (Alnus rubra Bong.), and Pacific

madrone (Arbutus menziesii Pursh).

The matrix model in WestPro predicts growth, mortality, and ingrowth for softwoods and

hardwoods as a function of basal area, site index, and individual tree size when those

variables are statistically significant. The WestPro program also employs equations to

predict volume from tree characteristics and stand basal area. Appendix B summarizes

the equations and their parameters.

The dependent variables for the four equations were:

• The diameter growth rate of each tree, in inches per year, estimated from the

difference in diameters at the time of the two inventories, divided by the number of

years between inventories.

• The tree mortality between the two inventories, recorded as a binary variable: 1 if a

tree had died, and 0 if it stayed alive.

• The ingrowth, or the number of trees per acre per year entering the smallest diameter

class between the two inventories, measured on each plot.

• The tree volume, in cubic feet, recorded in the FIA database.

The explanatory variables were:

• The individual tree size, measured as diameter at breast height in inches, at the first

inventory.

• The site index, measured by the height, in feet, of the dominant tree on the plot at

age 50.

• The stand basal area, in square feet per acre, of all the trees of diameter larger than

3 inches on the plot in which a particular tree was growing.

The summary statistics for all the variables are in table 1. The data from Washington and

Oregon have been combined because there was no statistical difference in the model

parameters between the two states, except for the hardwood growth equation, which

showed a slightly faster growth in Washington (see table 2 in app. B).

Appendix A—

WestPro Data
22

Table 1—Summary statistics for tree and plot data used in parameter estimation

 Diameter growth Diameter

Softwoods Hardwoods Softwoods Hardwoods Site index Basal area

– – – – Inches per year – – – – – – – – – – Inches – – – – – – Feet Square feet

per acre

Mean 0.19 0.10 17.43 11.55 95.96 150.71

S.D. .12 .09 10.14 6.54 23.41 66.47

Max .69 .62 64.09 38.23 145.93 353.13

Min .00 .00 3.03 3.03 47.21 52.95

 – – – – – – – – – – – – – – – – – – – – – – – – Sample size – – – – – – – – – – – – – – – – – – – – – – – – –

N 1,387 187 1,387 187 66 66

Mortality rate

(between inventories) Ingrowth Tree volume

Softwoods Hardwoods Softwoods Hardwoods Softwoods Hardwoods

– – – – – – – – – – – – Trees per acre per year – – – – – – – – – – – – – – – – – Cubic feet – – – –

Mean 0.04 0.10 1.99 0.74 103.03 35.27

S.D. .19 .30 4.81 2.31 123.13 46.17

Max 1.00 1.00 30.48 13.41 967.83 383.00

Min .00 .00 .00 .00 .80 .50

– – – – – – – – – – – – – – – – – – – – – – – – – Sample size – – – – – – – – – – – – – – – – – – – – – – –

N 1,472 271 66 66 1,375 161
23

The growth model uses a density-dependent matrix form, similar to that used by Lin et

al. (1998) and Kolbe et al. (1999).

t t t t t y = G y − h + I + ( ) 1 , (1)

where yt is a column vector representing the number of live trees per acre, yt=[yijt], where

i is the tree species, j is the diameter class, and t is the year. The column vector ht=[hijt]

represents the number of trees of species i and diameter class j harvested in year t. The

growth matrix Gt is defined as:





 



 =

t

t

t

2

1

G

G

G , with:

































=

− −

int

, 2, , 1,

1 2

1

0 a

b a

b a

a

i n t i n t

i t i t

i t

Git

 , (2)

where n is the number of diameter classes, bijt is the probability that a tree of species i

and in diameter class j at t is alive and in diameter class j+1 at t+1, while aijt is the probability that the same tree is alive and still in diameter class j at t+1. The subscript t indicates that the probabilities a and b vary over time because they are functions of stand

density.

If we let the mijt be the probability that a tree of species i and diameter class j dies between t and t+1, then aijt is given by:

aijt = 1- bijt - mijt . (3)

The ingrowth matrix, I

t

, is a column vector that contains the ingrowth for each species

group at time t.





 



 =

t

t

t

2

1

I

I

I , (4)

where I

it is the ingrowth of species i, that is the number of trees that enters diameter

class 1 between year t and year t+1. The subscript t indicates that the ingrowth varies

over time because it, too, is a function of the stand density.

The probability that a tree stays alive and moves from diameter class j to j+1 between

years t and t+1 is:

d

g b ijt

ijt = , (5)

Appendix B—

WestPro Model and

Parameters

Growth Equation

Growth Model Structure
24

where gijt is the yearly growth (in inches) of a tree of species i in diameter class j, and d

is the width of a diameter class (2 inches). In turn, gijt is a function of tree diameter, diameter squared, site index, and stand basal area. The parameters of this function, estimated with the data described in appendix A are in table 2.

The probability, mijt, that a live tree of species i and diameter class j died between year t

and t+1 was computed as:

T

m

m ijT

ijt = , (6)

where mijT is the probability that a tree dies between year t and t+T, the interval between

inventories, set at 10.6 years, the average interval between inventories across all plots.

mijT was represented by the logit function:

ijT

ijT

z

z

ijT

e

e

m

+ =1 , (7)

where zijT is a function of tree diameter, diameter squared, site index, and stand basal

area. The parameters of this function are shown in table 3. For this and other equations,

only variables that were statistically significant or conformed with a priori expectations

were included. Where none of the explanatory variables was statistically significant or

had the expected signs, the dependent variable was assumed to be constant, and set

equal to the mean observed in the sample.

Although more complex ingrowth equations were tried during the empirical work, the final

version of the model of ingrowth, in trees per acre per year, was a linear function of stand

basal area only. The parameters of the ingrowth function are in table 4.

The equation used to predict tree volume expressed volume in cubic feet as a function of

tree diameter, diameter squared, site index, and stand basal area. The parameters of the

tree volume equations are in table 5 for trees of at least 5 inches in diameter. The volume

of smaller trees was set equal to zero.

Table 2—Parameters of diameter growth equations

Explanatory variable

Species Diameter

group Constant Diameter squared Site index Basal area Statea

Inches Square inches Feet Square feet

per acre

Softwoods 0.035 0.0090 -0.00015 0.0016 -0.00055

Hardwoods .020 .0044 -.00011 .0008 -.00009 -.035

a 0 for Washington, 1 for Oregon.

Mortality Equation

Ingrowth Equation

Tree Volume Equation
25

Table 3—Parameters of logit model for probability of tree mortality between

two inventories

Explanatory variable

Diameter

Species Constant Diameter squared Site index Basal area

Inches Square inches Feet Square feet

per acre

Softwoods -2.42 -0.23 0.0034 0.0082 0.0029

Hardwoods .0996

Table 4—Parameters of ingrowth equation

Species Constant Basal area

Square feet

per acre

Softwoods 2.65 -0.0044

Hardwoods .74

Table 5—Parameters of tree volume equations

Explanatory variable

Diameter

Species Constant Diameter squared Site index Basal area

Inches Square inches Feet Square feet

per acre

Softwoods -64.8 -0.18 0.221 0.46 0.080

Hardwoods -23.5 -.94 .22 .24 .01
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